https://doi.org/10.1140/epjc/s10052-016-4525-7
Regular Article - Theoretical Physics
Cosmic constraint on massive neutrinos in viable f(R) gravity with producing 
CDM background expansion
1
Department of Physics, Liaoning Normal University, Dalian, 116029, People’s Republic of China
2
Department of Physics, Xinyang Normal University, Xinyang, 116029, People’s Republic of China
* e-mail: lvjianbo819@163.com
Received:
11
June
2016
Accepted:
20
November
2016
Published online:
8
December
2016
Tensions between several cosmic observations were found recently, such as the inconsistent values of 
(or 
) were indicated by the different cosmic observations. Introducing the massive neutrinos in CDM could potentially solve the tensions. Viable f(R) gravity producing CDM background expansion with massive neutrinos is investigated in this paper. We fit the current observational data: Planck-2015 CMB, RSD, BAO, and SNIa to constrain the mass of neutrinos in viable f(R) theory. The constraint results at 95% confidence level are: 
eV for the active-neutrino case, 
eV with 
for the sterile neutrino case. For the effects due to the mass of the neutrinos, the constraint results on model parameter at 95% confidence level become 
and 
for two cases, respectively. It is also shown that the fitting values of several parameters much depend on the neutrino properties, such as the cold dark matter density, the cosmological quantities at matter–radiation equality, the neutrino density and the fraction of baryonic mass in helium. Finally, the constraint result shows that the tension between direct and CMB measurements of 
gets slightly weaker in the viable f(R) model than that in the base CDM model.
© The Author(s), 2016
